How can I export my Google Scholar Library as a BibTeX format?

As of August 31, 2016, this functionality has been added! See this blog post: https://googlescholar.blogspot.com/2016/08/organizing-your-scholar-library.html

I can only add that you can download citations one by one:

• in Settings > Bibliography Manager, check Show link to import citation into BibTex.

With that, you can probably write a script (maybe using Scholar.py) that downloads all your citations. An example URL is:

http://scholar.google.com/scholar.bib?scila=u_35RYKgDlwC&output=citation&hl=en&ct=citation&cd=1

You can use the scholar R package. I copied this answer from this tweet, in R

install.packages("scholar")
library(scholar)

ID <- "Put your id from pic below in here"
pubs <- get_publications(ID)
write.csv(pubs, file="citations.csv")

There may be another package which allows you to write out bibtex.